Shor-code phase-flip syndrome
ID: shor-code-phase-flip-syndrome
Group the nine physical qubits into three blocks and write for the product of three Pauli X gates in block . The commuting stabilizer generators and have eigenvalue on both logical codewords. A Pauli Z gate in blocks one, two or three gives syndromes , or respectively. Apply a Z gate to any one qubit of the indicated block to recover the logical state. Z errors at distinct locations within a block act identically on the code, so this correction is degenerate.
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